1. Field
The present disclosure relates generally to apparatus and methods for computing constant amplitude zero auto-correlation sequences, and more specifically to real-time computing of Zadoff-Chu sequences for preambles in a communication system.
2. Background
In cellular communications, the physical random access channel (PRACH) is a common uplink channel used by mobile users within a cell to establish initial access to a base station, along with uplink synchronization to compensate for round-trip delays to the base station. The mechanism is based on the mobile user equipment (UE) transmitting a randomly-chosen preamble to a base station (e.g., eNodeB) over a dedicated time-frequency resource on the PRACH, such as in the emerging Third Generation Partnership Project (3GPP) long-term evolution (LTE) physical layer standard. A pool of known preambles is allocated to a base station within a cell. A PRACH processor, or searcher, in the base station attempts to detect a transmitted preamble by first extracting the PRACH signal from a received wideband OFDM signal, then performing matched filtering across the pool of preambles allocated to the base station. The matched filtering is performed as a cross-correlation of the extracted PRACH signal with each of the known preambles dedicated to the base station. The cross correlations provide a final metric that is compared to a threshold, from which the presence of a preamble can be detected and the mobile user's timing offset relative to the base station can be estimated.
An important requirement is that the system must be capable of supporting a large number of users per cell with quasi-instantaneous access to the radio resources, and sustain a good detection probability, while maintaining a low false alarm rate. Hence, preambles must be constructed using sequences that possess good periodic correlation properties. One candidate sequence is the well-known Zadoff-Chu (ZC) sequence, which belongs to a class of sequences called constant amplitude zero auto-correlation (CAZAC) sequences. These sequences are currently employed in the emerging LTE PHY layer standard to construct PRACH preambles. ZC sequences are complex exponential codes whose discrete auto-correlations are zero for all non-zero lags, with no restrictions on code lengths. A disadvantage, however, is that ZC sequences are difficult to generate in real-time due to the nature of their construction. Known implementations typically resort to pre-computing these sequences off-line, quantizing them to the required precision, and storing them in memory. For example, in LTE with 3-sector cells where a pool of 64 preambles of length 839 are allocated to each sector (Format-0 preambles), a memory storage of 2.5 M-bits is needed to store these complex-valued sequences, assuming 8-bit quantization. In the case of LTE, the standard must also support preambles of length 139, so the total memory needed is around 3 M-bits. Accordingly, in one aspect it would be desirable to reduce need for storing ZC sequences, such as through efficient generation of ZC sequences in real-time.